Mystery in The Air

After this storm cloud, there came another, which produced only little roses or wheels with six rounded semicircular teeth … which were quite transparent and quite flat … and formed as perfectly and symmetrically as one could possibly imagine. There followed, after this, a further quantity of such wheels joined two by two by an axle, or rather, since at the beginning these axles were quite thick, one could as well have described them as little crystal columns, decorated at each end with a six-petalled rose a little larger than their base. But after that there fell more delicate ones, and often the roses or stars at their ends were unequal. But then there fell shorter and progressively shorter ones until finally these stars completely joined, and fell as joined stars with twelve points or rays, rather long and perfectly symmetrical, in some all equal, in others alternately unequal. (1)

The beauty, symmetry and diversity of snow crystals have long fascinated scientists. Snow crystals come in endless variety of six-fold symmetric shapes, sometimes thinner than a sheet of paper and up to 3 millimeters across. How can they grow in a three dimensional bath and yet be thin? What natural processes could lead to great diversity of shapes that are complex yet symmetric? What keeps opposite sides of the growing crystal in step even as a unique shape is forming? And with slightly different temperature or humidity produces sensible hexagonal columns instead? Is there any rational explanation for the generation of these crystals out of thin air? Can you formulate a hypothesis that even has a chance?

The Japanese scientist Ukichiro Nakaya, working in the nineteen thirties through nineteen fifties was the first one to develop methods to grow individual snow crystals under carefully controlled conditions. (2) Nakaya had intended to be a nuclear physicist, but he got a professorship on the Japanese island of Hokkaido where there no nuclear facilities. There was, however, lots of snow. Nakaya’s 1954 book, Snow Crystals, Natural and Artificial, “…offers a superb look at a scientific investigation which begins with almost nothing, and proceeds through systematic observation toward an accurate description of a fascinating natural phenomenon.” (2) Most of his experimental discoveries are summarized in what is now called the snow crystal morphology diagram.

The morphology diagram does not show all possible types of snow crystals. It shows only shapes that grow under fixed conditions. But knowing both the morphology diagram and that natural snow forms in turbulent storm winds gives us a big boost toward understanding how such diverse yet symmetric shapes are formed. Each crystal follows its own essentially random path through the sky and hence through conditions that will stimulate different sorts of growth, and so gains a different form. Conditions do not vary significantly over the size of a crystal though. So each crystal takes on a different symmetric form.

Nakaya’s work beautifully lays out the snow crystal puzzle. Now all we have to do is solve it. In very broad terms snow crystals happen the way other things happen in nature, especially things with complex symmetry. They result from a combination of natural regularities, surprising threshold effects, and a sequence of frozen accidents. But what are the regularities and nonlinearites? How does it happen, for instance, that at a supersaturation of around .1 g per cubic meter, crystals are (with decreasing temperature) hexagonal plates, then columns, then plates, then columns again? How can the morphology diagram be explained?

This is what physicist Ken Libbrecht is trying to find out. While Christmas shopping last month I couldn’t help noticing the beautiful snow crystal on the cover of the new American Scientist. This led me to Libbrecht’s article The Formation of Snow Crystals (3). The article was quite intriguing, but there was a key point I couldn’t follow. On page 57 he seems to say that his experimental measurements of the growth velocity of different facets were contrary to what the morphology diagram predicts, yet the diagram is still correct. How could this be? This led me to read his The Physics of Snow Crystals (4), a mere forty pages with one or two equations, and then another paper with actual data (5). Finally I gained some idea of what’s going on.

But to begin at the beginning: warm moist air rises and rises until it expands and cools. Cold air can hold less water vapor than warm air, and so, especially if the air becomes very cold, it will become supersaturated with water vapor. Air is full of vast numbers of tiny dust particles; very tiny water droplets form on these particles. Even well below the normal freezing point, these droplets do not freeze into ice, but instead most persist as supercooled water. Different ones freeze at different temperatures, due in part to the surface characteristics of their dust particle. Those that freeze may grow into snow.

The minute supercooled liquid droplets have so much surface area in relation to their volume that they are constantly evaporating and reforming. Once a vapor molecule sticks to an ice crystal, though, it tends to stay there. Thus the crystals grow at the expense of the droplets. The droplets are so small that a good sized snow crystal may have consumed a million of them (3:52). To a first approximation, crystal growth is diffusion limited A growing crystal uses up nearby vapor molecules and cannot grow larger until more vapor diffuses to it.
Early in its growth nearly every snow crystal experiences faceting. This is a normal feature of crystal growth in which rough spots smooth out and the crystal takes on a characteristic shape with several plane faces, or facets. For ice crystals in normal winter conditions, this shape is a hexagonal prism.

Growth of the crystal facets. Once a crystal takes on this basic shape, growth tends to be normal to the facets, at least as long as growth is not too fast and the crystal is not too large, say less than half a millimeter across. Growth is controlled by attachment kinetics, which is in turn controlled by the still mysterious surface physics of the growing snow crystal.

Modern equipment makes possible measurements Nakaya couldn’t make, including the growth rate of individual facets. This measurement is important because of its quantitative relation to other factors. But it isn’t easy: “… a critical examination of the literature reveals that essentially all the results published to date suffered from systematic errors to some degree.” (4:878) On the basis of recent measurements though, Libbrecht suspects that growing snow exhibits a previously unknown type of instability - which brings me back to the unexpected data I mentioned earlier.

Low pressure is the key - to normal crystal growth. When grown at -15 degrees Centigrade and high supersaturation, right where the morphology diagram predicts the thinnest crystals, but at less than one quarter of normal atmospheric pressure, all the facets grow at about the same very slow rate and the crystals look blocky and ordinary. But merely increase the pressure and the prism facets (but not the basal facets) start growing up to 50 times faster! How can ordinary air have this effect? Libbrecht gives a very partial explanation in (5): a thin but growing facet is expected to have a parabolically curved edge, with a small radius of curvature. The radius is inversely proportional to pressure according to a certain formula that can be derived with some simplifying assumptions. Compared to a flat crystal surface, this curved surface will be rough on a molecular scale. This makes it easier for some ice molecules to form hydrogen bonds with passing vapor molecules and hold on to them. Evidently, when there is enough pressure, and hence enough curvature, growth becomes much faster. Libbrecht refers to this as a knife edge instability resulting from structure-dependent attachment kinetics.

As Libbrecht says, “This is a speculative model, without a strong theoretical foundation, so additional work is needed to understand this aspect of the growth dynamics.” (4:881) But as he explains, the knife edge instability is consistent with both the crystal growth data at different pressures and notable features of natural snow. These features include the extreme thinness of large stellar crystals (about .01 millimeter) and the abrupt transition observed in capped columns (see the first illustration). “… instabilities tend to amplify small changes in initial conditions. If the local environment changes just slightly to prefer platelike growth over columnar growth, then the instability kicks in to immediately produce thin plates.” (3:58)

Branching and dendritic growth. Growing perpendicular to the facets is not the only way snow grows. Snow crystals are famous for their complex branched and dendritic forms. This type of growth too has been modeled and studied experimentally. As each crystal facet expands, its center is slightly starved of vapor molecules compared to its corners. This makes the facet just slightly convex although it looks flat to the eye. The convexity, greatest at the center, amounts to roughness on the molecular scale - the scale where the action is. This roughness leads to a little greater percentage of incident vapor molecules sticking to the crystal, and so the center’s growth keeps up with the corners - until it doesn’t. When the crystal is large enough, say about half a millimeter across, and/or growth is fast enough, branches spout from the six corners of the hexagon. This is called the Mullins - Sekera instability, or simply the branching instability.

The corner branches may become long dendrites; these may sprout dendrites of their own, or in other conditions may even sprout six new flat plates. A dendrite’s rate of elongation, and hence rate of vapor consumption, may become so great that the growing tip is in a region of reduced vapor density. Nonetheless the highly curved, and hence molecularly rough, tip keeps on growing. Dendritic growth is observed in other sorts of crystals and is thought to be fairly well understood. Snow crystal branches and dendrites are unusual, though, in that they retain their basal non-growing facets. Faceted dendrites are not so well understood. (4)

Has the challenge of the morphology diagram been met? There is reason for optimism about future research. The identification of systematic errors in previous experimental data should result in more precise data in the future, and the structure-dependent attachment kinetics hypothesis is a promising lead. But for now, the explanation (above) of capped columns, for instance, includes these words: “If the local environment changes just slightly to prefer platelike growth over columnar growth .…” But why would a slight change in conditions have this effect? That was the question. In the end Libbrecht admits

The growth of plain hexagonal ice prisms remains perhaps the most puzzling aspect of snow crystal growth, in spite of its apparent simplicity. The snow crystal morphology diagram, well documented now for 75 years, has still not been explained at even a qualitative level. (4:891)

Get to Ken Libbrecht’s www.snowcrystals.com to find lots of activities, movies and books on snow crystals. There is no snow in my neighborhood, but I’m interested in hearing your experiences. Can anyone match Descartes’ observations, even with the help of a hand magnifier?

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35 Comments

When I was at the University of Michigan back in the late 1970s and early 1980s, Len Sander (http://www.lsa.umich.edu/physics/pe[…].html?ID=283) was modeling this kind of thing on the computer and producing some remarkable results. He is still at it and has extended his research to biological systems as well.

With all of the mixed up “religion” out there, I can understand your aversion to it.
You are in good company, by the way, God reserved His greatest condemnation for “religious” people who lead people away from the Truth with their own man-made views.
If you look at the scientific data with an open mind, however, I do believe it leads you to the undeniable conclusion that there is an all-powerful and infinitely wise Creator behind it all - not an explosion.

19 � Because that which may be known of God is manifest in them; for God hath shown it unto them.
20 For the invisible things of Him from the creation of the world are clearly seen, being understood by the things that are made, even his Eternal power and Godhead; so that they are without excuse. Romans 1:19-20

I understand how this sounds to you, because, when you are taught that something is true (evolution) all your life, you tend to believe it - even if truly, the evidence is missing. I have always been very interested in science and have gathered a lot of information on this topic on the link
“Evolution or Creation, What are The Scientists Saying?” which can be reached from the page www.Godhastheanswer.com.
Please just give it a look with an open mind - I look forward to hearing your feedback.
-Ed

Here’s some feedback for you, Ed. I’ll confine myself to the document you mention.

In the first sentence under the head A I count three obvious errors, demonstrating that you have no knowledge of physics. In the last sentence of the that paragraph I count four more, demonstrating that you have no knowledge of biology.

What you think you are doing, writing about either subject, I cannot imagine.

Your quote mines are the usual nonsense. Most of them only go to prove that the scientists quoted were not in the least hostile to religious belief, and hence actually undermine your own position. But some are outrageous. For example, the first Darwin quote only demonstrates his own humility, and to use it to attempt to insinuate that he doubted his own theory is a subtle and contemptible lie. The second states his willingness to defend his theory in the full, hard light of the facts, a process which it has been undergoing for a hundred and fifty years, and triumphing. The Whitten quote is a quote mine, and misrepresents him. Whitten wrote later: “saying anything that would support creationism could not have been further from my mind. Of course, my whole working life have been around a Darwinian framework.”

Other lies: the number of scientists who doubt evolutionary theory is not growing, and almost all of the tiny proportion of those that do doubt it work in fields irrelevant to biology. The ID crowd are not scientists (they don’t do any science).

Evolution does not predict increasing complexity in populations, only change by natural selection, which may favour less. It does not predict “defective forms” in the fossil record - that’s Gish being ignorant and mendacious, as Gish is. There are, however, very large numbers of fossils showing forms transitional between groups. You say rightly that creationism would not predict this. Why do you ignore the ones that exist, then?

The quote mines that purport to lament the lack of “intermediate forms” in the fossil record are straightforward misrepresentations of the statements of scientists who cite these concerns and then go on to refute or explain them, and they date from the seventies or earlier. Much more has been found since then.

Setting the Bible quotes aside, the rest consists of the arguments from complexity and ignorance. These were long, long ago shown to be the foolish nonsense that they are.

Some howlers: you have managed to discuss the transition from fish to tetrapods without even a nod at the half-dozen transitional forms now known, by quoting a textbook written in 1974! This may be no more than an exhibition of shameful ignorance, but its effect is to promulgate an untruth. Your remarks about human evolution are worse, if anything. To say that no transitional forms exist in the face of Australopithecus afarensis, A. africanus, Homo habilis and H erectus requires more than ignorance. It requires a total refusal to look facts in the face, or wilful mendacity, or both.

And of course, the real killer is the utter refusal to show evidence for special creation. All of your arguments against evolution are unsound, faulty, based on lies, misinformation or misunderstanding, but even setting that aside, you show no evidence from nature for the separate creation of the species, and a total inability to grasp that some is required.

In short, your document is sheer nonsense from beginning to end. Do a little reading outside creationist tracts. Try to learn a little. It’ll do you good.

With all of the mixed up “religion” out there, I can understand your aversion to it

I have no aversion to religion, I simply find its claims uniformly unfounded and without practical use of any kind. What I do have an aversion to is the religiously-inspired dissemination of fallacy, illogic and lies so often perpetrated the religious in their attempts to resolve discrepancies between their silly superstitions and reality. Your link to that awful collection of anti-scientific garbage is a prime example of this.

Your Bible is not a science book, and the findings of science are not a statement about your religious beliefs or anyone else’s. It’s your choice to conceive of religion and science as inimical to one another, and in implementing this choice you show that you have a very poor grasp of the relevant concepts of either. The world would be better off with a lot less of the kind of religion you’re here to peddle, and it gratifies me to see what a good job you’re doing to turn people off to your kind of dogma, by spreading such baldly inept dishonesty. Keep it up.

I understand how this sounds to you, because, when you are taught that something is true (evolution) all your life, you tend to believe it - even if truly, the evidence is missing.

Interesting assumption on your part, Ed. As usual, such assumptions reveal more about the writer than about the targeted reader.

I can’t speak for anyone else here, but I have never been taught that “evolution is true”. I’ve been shown a lot of evidence for evolution, and I’ve even done comparative morphology, and fossil hunting, and isotopic dating experiments to find such evidence myself. Through examining that evidence I’ve become convinced that evolution is the most effective explanation we have today for the living things we see around us.

But I’m also convinced that tomorrow we will have more evidence than we have today. Tomorrow we will have more explanations than we have today. Perhaps this new evidence and explanation will modify evolution, just as Einstein’s relativity modified Newton’s mechanics.

So I have never been taught that evolution is “true” and I certainly don’t “believe” in evolution – evolution is not based on faith, so evolution is not a belief.

On the other hand I have been taught that all science is tentative, and I do believe that because I’ve seen scientific generalizations held for decades overturned because of good evidence against them.

I have been taught that all science is tentative, and I do believe that because I’ve seen scientific generalizations held for decades overturned because of good evidence against them

Good point. Ed, the history of science is rife with examples of established theories being destroyed or heavily revised based on the discovery of new evidence. Were someone able to amass and cohere such evidence for a theory that explained the facts better than evolution does, their place in scientific history would be exalted and assured.

The problem with your position, and that of your fellow creationists , is that none of you are proposing scientifically valid alternate hypotheses, and none of you are actively looking for the kind of evidence that would be needed to overturn evolution. This needs to be done by proposing and supporting a better theory, not by posting ignorant anti-evolution screeds peppered with bible quotes on slow, balky internet servers. All I see on the page you linked, and in the total content of all contemporary creationist output, is attempts to use existing evidence to prove that evolution could not be true. This presents many problems, including the following.

First, this employs a false dilemma; valid argument and evidence against the theory of evolution does nothing, nothing, to support your or any other theory (and you do not present one). It only speaks to the validity of evolution. And since creationists fail to express any scientifically testable hypotheses (save ones which have already been falsified in the past), there is nothing to support in any case. You bible is not a scientific argument, and nothing in it constitutes useful scientific evidence for anything outside the field of history. Second, all of these efforts are invariably rife with fundamental, intentional misunderstandings and misconstruals of what evolution claims, vast misrepresentations of the existing evidence, and rampant logical flaws which render your arguments incapable of showing the validity of your ideas, or indeed any idea.

I consistently see the same fatal logical fallacies deployed throughout your literature: Argumentum ad populum: “Evolution must be false because so many people “believe” otherwise”; False Dilemma (as above): “Evolution must be false because creationism is true”, which can only be valid if you can demonstrate that there are only two possible choices; Argument from consequences: “Evolution must be false because accepting it as true leads to Hitler, lack of morals, etc.”; Argument from incredulity: “Evolution must be false because I can’t see how it is possible”; Argument from ignorance, special pleading, the list of fallacious arguments deployed by creationists go on and on.

If you and yours think you have a scientific case to make, make it. State logically sound, testable, falsifiable hypotheses of when, where, and how life was ever created, and test them; attempt to falsify them. That is how science works; if you are not wiling to subject your ideas to potential falsification, You. Are. Not. Doing. Science. And if you’re not doing science, you have no right to complain about the results of the scientific method, TOE among them.

A stupid person looks for evidence their ideas are right. A smart person looks for evidence their ideas are wrong. If you have a good idea, and you subject it in good faith to every attempt you can think of to show that it is wrong, and you cannot do it, you can expect others to accept that your idea has merit (and you can also expect them to begin to test your idea as well). Creationists make no attempt to do this (because they have no ideas which they can conscience the potential falsification of, as this would in their minds falsify their god), and that is why they are ridiculed here–because, no offense, you are that stupid person. That is why you can expect to be ridiculed here, until you show you are really interested in science, and not just in co-opting the accepted explanatory power of science’s methods in support of your narrow, idiosyncratic superstitions.

Man these religious folks have the answer to everything. Sure, every little snowflake is carefully designed by God himself, while He was taking a break from exploding galaxies 10 billion light years from here. (This we will find out in ten billion years, because not all astronomers were burnt.) The very fact that He has time for carefully designing each and every little snow flake proves His Existence. After all no monkey or decendant thereof could do this. QED!

a correction to my above statement, has to do with the word unbelief.don’t direct the word unbelief (anti-Christ)but direct, belief, in the Lord Jesus Christ. i would suggest to anyone that does not believe, to ask himself,or herself this question. Have I read,(studied) the book,Bible, namely the new testament as a result of my unbelief? The answer most likely, is no, I haven’t. I suggest that you at least study it before passing judgment to your own peril. the moment anyone directs his or her belief in the Lord Jesus Christ, a most amazing and wonderful transition takes place.Try it,(Him,you’ll like it,(Him).

I understand how this sounds to you, because, when you are taught that something is true (evolution) all your life, you tend to believe it - even if truly, the evidence is missing. I have always been very interested in science and have gathered a lot of information on this topic on the link
“Evolution or Creation, What are The Scientists Saying?” which can be reached from the page www.Godhastheanswer.com.
Please just give it a look with an open mind - I look forward to hearing your feedback.
-Ed

Ed,

I was raised to believe in creation. I found out that there is no evidence for that idea. I found out that the evidence is overwhelmingly in favor of evolution. This is not because of the way that I was raised. If you do not understand biology, don’t presume to tell others what the evidence is. I would suggest that you increase your knowledge.

a correction to my above statement, has to do with the word unbelief.don’t direct the word unbelief (anti-Christ)but direct, belief, in the Lord Jesus Christ. i would suggest to anyone that does not believe, to ask himself,or herself this question. Have I read,(studied) the book,Bible, namely the new testament as a result of my unbelief? The answer most likely, is no, I haven’t. I suggest that you at least study it before passing judgment to your own peril. the moment anyone directs his or her belief in the Lord Jesus Christ, a most amazing and wonderful transition takes place.Try it,(Him,you’ll like it,(Him).

I have studied the new testament extensively. I find that it teaches some great moral lessons. However, I find that it is completely worthless as a science text, so I don’t use it for that. I have no problem in anyone believing in any religion they choose, just don’t try to substitute it for science in a public school science class.

A) There is a big difference between discarding a scientific theory because of new, contradictory evidence, and discarding a scientific theory because of the alleged possibility of new, contradictory evidence

and

B) There are literal millions of examples of people who have no problem accepting Jesus and accepting the fact of evolution.

i would suggest to anyone that does not believe, to ask himself,or herself this question. Have I read,(studied) the book,Bible, namely the new testament as a result of my unbelief? The answer most likely, is no, I haven’t. I suggest that you at least study it before passing judgment to your own peril. the moment anyone directs his or her belief in the Lord Jesus Christ, a most amazing and wonderful transition takes place.Try it,(Him,you’ll like it,(Him).

There are literally billions of people out there who would challenge you to do the same with their thousands of various scriptures and alleged gods, most of which fundamentally conflict with yours and with each other. Have you studied their books? Are you not worried about the peril they claim you’re risking by passing your own judgement on what god is the correct one? Get your head out of the sand and STFU about what other people choose to believe about god, or the lack thereof. Try it, we’ll like it.

i would suggest to anyone that does not believe, to ask himself,or herself this question. Have I read,(studied) the book,Bible, namely the new testament as a result of my unbelief? The answer most likely, is no, I haven’t. I suggest that you at least study it before passing judgment to your own peril.

The irony in this statement is apparently lost on this proselytizer.

He needs to look in the mirror and ask the same questions of himself regarding science.

Man these religious folks have the answer to everything. Sure, every little snowflake is carefully designed by God himself, while He was taking a break from exploding galaxies 10 billion light years from here. (This we will find out in ten billion years, because not all astronomers were burnt.) The very fact that He has time for carefully designing each and every little snow flake proves His Existence. After all no monkey or decendant thereof could do this. QED!

You would think God would get bored having to order 10^22 atoms of water in each of billions of snowflakes.

Stuart Weinstein said:
You would think God would get bored having to order 10^22 atoms of water in each of billions of snowflakes.

Maybe it’s not God.

Maybe Satan is behind it.

Could I now but catch him dying,
Sure of heaven as sure could be
Spin him ‘round and send him flying,
Off to Hell, a Manichee! (Browning, “Soliloquoy in a Spanish Cloister”)

Manicheanism, the idea that Satan must be partly or wholly responsible for creating the world, since there is manifestly evil in it. Condemned as a heresy at the Nicean Council, because it necessarily implies that God is not the only Creator. (That’s the reason for the line in the Creed about creating all things visible and invisible.)

No, no. God creates the snow. And blizzards. And avalanches. All that. And while He was at it, chiggers and tapeworms and typhoid and the plague and the HIV virus and the Queensland box jellyfish. Plus lots of other cute stuff.

And when I ask the clergy about this little quirk God appears to have, what I get is a meaningful silence, followed by something like, “Ah, yes, theodicy. There are some things Man was not meant to know.” Or words to that effect, fade in “The End” with a question mark, roll credits.

I think God has allowed the universe to have an independent nature, somehow between light and darkness, good and evil, with both having an influence, and evil is a result of allowing independence from good within the created universe. If you could not choose to do nasty stuff, you could not choose to really love someone either. Part of you living in a universe where everything is not controlled directly by God, means choice, independence from God, and evil have an outcome and impact, all be it temporarily.

So how do you account for, say, muscular dystrophy, Ed? Doesn’t allow the sufferer a whole lot of independence, and here’s the thing: the most severe forms occur in early childhood, and the worst affected die in early adolescence, after years of severe and progressive disability and pain.

If that’s God’s doing, He’s got some explaining to do, for mine. Even if it’s not, and it’s only that He won’t or can’t stop it, the same applies. If he won’t, he’s a monster. If he can’t, some God that is.

So how do you account for, say, muscular dystrophy, Ed? Doesn’t allow the sufferer a whole lot of independence, and here’s the thing: the most severe forms occur in early childhood, and the worst affected die in early adolescence, after years of severe and progressive disability and pain.

If that’s God’s doing, He’s got some explaining to do, for mine. Even if it’s not, and it’s only that He won’t or can’t stop it, the same applies. If he won’t, he’s a monster. If he can’t, some God that is.

Good point, and any answer can sound like a cliche as it is easy to talk of other peoples pain when you are not suffering yoursef. I do believe in a loving God, mainly because of experience and supernatural evidence, which gives me hope in a bigger picture, where human beings have another dimension beyond the physical and tempoaray. Also a temporarily and partially independent universe has temporarily unfair outcomes, and we frequently add to that unfairness. Part of that independence is the human choice to procreate - and bring others into this risky world. Millions of people appear to believe it is worth it. I have been hasty in my reply as I am submitting a masters thesis today! I will come back and hopefully engage more fully soon.